Engineering Board Exam Reviewer · Linear First-Order Differential Equations · hard

Solve xdy/dx+y=x2 for x>0.

1. y=x2/3+C/x
2. y=x2/3+C
3. y=x3/3+C/x
4. y=x/3+C/x

Answer

A. y=x2/3+C/x

Solution

Rewrite as dy/dx+y/x=x. The integrating factor is =x: (xy)'=x2 xy=x3/3+C y=x2/3+C/x.

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1. Determine if dy/dx+y2=x is a linear differential equation.
2. Solve the linear differential equation dy/dx+y=ex.
3. Find the integrating factor for the linear differential equation dy/dx+2/xy=x3.
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